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2008 NeurIPS NeurIPS 2008

Convergence and Rate of Convergence of a Manifold-Based Dimension Reduction Algorithm

Abstract

We study the convergence and the rate of convergence of a local manifold learning algorithm: LTSA [13]. The main technical tool is the perturbation analysis on the linear invariant subspace that corresponds to the solution of LTSA. We derive a worst-case upper bound of errors for LTSA which naturally leads to a convergence result. We then derive the rate of convergence for LTSA in a special case.

🌉 Interdisciplinary Bridge - Artificial Intelligence and Mathematics & Optimization

📈 Trend Setter - Geometry

🧭 Keyword Pioneer - perturbation analysis

🐣 Hot Topic Early Bird - convergence rate

Authors

Andrew Smith, Hongyuan Zha, Xiao-ming Wu

Topics

Machine Learning > Core Methods > Representation Learning Machine Learning > Optimization & Theory > Learning Theory Machine Learning > Optimization & Theory > Theory Mathematics & Optimization > Mathematics > Geometry Machine Learning > Core Methods > Dimensionality Reduction

Keywords

dimensionality reduction manifold learning subspace learning convergence analysis dimension reduction local tangent space perturbation analysis ltsa convergence rate spectral method ltsa algorithm local tangent space alignment

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